Classroom Simulation: False Indications of Ouliers in Boxplots of Normal Data

• Activity Number: 76
• Type: Contributed
• Date/Time: Sunday, August 6, 2006 : 8:00 PM to 9:50 PM
• Sponsor: Section on Statistical Education
• Author(s): Bruce E. Trumbo*+ and Eric A. Suess and Jacob Colvin
• Companies: California State University, East Bay and California State University, East Bay and California State University, East Bay
• Keywords: boxplot ; outlier ; simulation ; R/S-Plus ; pedagogy ; teaching undergraduates

Abstract

Computer packages often use boxplots of data to indicate "outliers": data values beyond fences located a certain multiple, often 1.5, of the interquartile range (IQR) on either side of the box bounded by the lower and upper quartiles. Simulation, presented here, shows that this definition of outlier yields surprisingly many false outlier indications in normal data of small or moderate sample size, and that the proportion of such indications is very sensitive to sample size. Simulation studies using R investigate the behavior of such outlier indications for several sample sizes, several multiples of IQR, and several parent populations. One behavior studied is the proportion of simulated samples with one or more outlier indications. Concepts and simulation programs are at a level appropriate for use in undergraduate statistics classes.